We consider the problem of recovering a sparse signal \(\mathbf {x}\)  from noisy measurements \(\mathbf {y} = \mathbf {Ax} + \mathbf {w}\) , where \(\mathbf {A}\)  is a known measurement matrix [1]}. This problem finds numerous applications in various areas of signal processing, statistics and computer science. One approach to recovering \(\mathbf {x}\)  is to use sparse Bayesian learning (SBL), where \(\mathbf {x}\)  is assumed to have a sparsity-promoting prior [2]}.
Conventional implementation of SBL involves matrix inversion in each iteration, resulting in prohibitive computational complexity for large scale problems.
